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What is the equation of a line that goes through $(7, - 7)$ $(7, -7)$ and has a slope of $- 3$ $-3$ ?

1 Answer

Nov 19, 2015

You use standard form of $y = m x + c$ $y=mx+c$ and substitute in the given values to find the value of c

$y = (- 3) x + 14$ $y =(-3)x+14$

Explanation:

Using $y = m x + c$ $y=mx+c$ and universal notation of $(x, y)$ $(x,y)$

Let $y = - 7$ $y= -7$
Let $x = 7$ $x=7$
Let $m = - 3 \times x$ $m=-3color(white)(xxx)$ (this is fixed. It does not change!)

Giving:

$- 7 = (- 3) (7) + c$ $-7=(-3)(7) +c$

$- 7 = - 21 + c$ $-7 = -21+c$

Add +21 to both sides:

$- 7 + 21 = - 21 + 21 + c$ $-7 +21 = -21+21+c$

$14 = 0 + c$ $14=0+c$

$c = 14$ $c=14$

So the full equation of the line is:

$y = (- 3) x + 14$ $y =(-3)x+14$

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